Although most works have relied on a time division duplex (TDD) design, recent results regarding IRS showed that the phase shifts depend on the angle of the impinging electromagnetic waves, which renders the assumption of channel reciprocity questionable [1]}, [2]}, [3]}. In particular, in [1]}, it was shown that channel reciprocity holds only when the incident angles are small while, in [3]}, several IRS-assisted approaches such as the time-varying control and the structural asymmetries, realizing non-reciprocal channels, were introduced. Hence, the study of the design and the performance of IRS-assisted systems, operating in frequency division duplexing (FDD), is required and is the motivation for the work presented in this paper.This observation has been also recognised in [2]} as one of the most interesting topics for future research. Note that many current wireless networks are based on FDD systems, which contributes further to our interest in such systems. Moreover, FDD operates more effectively in the cases of symmetric traffic and delay-sensitive applications [7]}. However, FDD cannot be easily deployed in 5G and beyond systems such as mMIMO because the multi-antenna channel acquisition makes their implementation prohibitive [8]}. In particular, FDD includes downlink training, which together with the CSI feedback, present a significant bottleneck as the number of BS antennas increases. Fortunately, the use of the joint spatial division and multiplexing (JSDM) approach allows achieving SE gains similar to mMIMO [9]} while it has not been applied yet in IRS systems.
